Presenting some impressive recent achievements in differential geometry and topology, this volume focuses on results obtained using techniques based on Ricci flow. These ideas are at the core of the study of differentiable manifolds. Several very important open problems and conjectures come from this area and the techniques described herein are used to face and solve some of them.The book’s four chapters are based on lectures given by leading researchers in the field of geometric a...

New methods for the determination of the nature, proportion, and distribution of structural defects in microcrystallized lamellar systems are of utmost importance not only to experimentalists but also to theoreticians. Mathematical formalism - indispensable for such analyses - is well-illustrated by various examples, allowing this method to be easily adopted and even to be applied to other solids with lamellar or pseudo-lamellar structures.

In crystal chemistry and crystal physics, the relations between the symmetry groups (space groups) of crystalline solids are of special importance. Part 1 of this book presents the necessary mathematical foundations and tools: the fundamentals of crystallography with special emphasis on symmetry, the theory of the crystallographic groups, and the formalisms of the needed crystallographic computations. Part 2 gives an insight into applications to problems in crystal chemistry. With the aid ...

Based on lectures given at Zhejiang University in Hangzhou, China, and Johns Hopkins University, this book introduces eigenfunctions on Riemannian manifolds. Christopher Sogge gives a proof of the sharp Weyl formula for the distribution of eigenvalues of Laplace-Beltrami operators, as well as an improved version of the Weyl formula, the Duistermaat-Guillemin theorem under natural assumptions on the geodesic flow. Sogge shows that there is quantum ergodicity of eigenfunctions if the geodesi...

Remarks by JVS. Volumes 1 and 2 of Feldspar Minerals were published in 1974, but Volume 3 was not completed because I was forced to devote 3 years to the resolution of unforeseen problems in the construction of an ion probe. By 1977, the incomplete draft for Volume 3 had become obsolete because of the enormous advances in knowledge of feldspars, particularly those in lunar rocks and meteorites, and in both deep-seated and ancient terrestrial rocks. Furthermore, it soon became obvious that ...

Arising from the fourth Dagstuhl conference entitled Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data (2011), this book offers a broad and vivid view of current work in this emerging field. Topics covered range from applications of the analysis of tensor fields to research on their mathematical and analytical properties.Part I, Tensor Data Visualization, surveys techniques for visualization of tensors and tensor fields in engineering, discu...

This book presents the third volume of a complete development of the new structural classification of minerals, which is based on the internal crystal structure, and is therefore its natural classification. Because of the large domain of the mineral kingdom, this work is divided in three volumes, in which the minerals are ordered from the structurally simple to the more complex.Audience: This work will be of particular interest to teachers and research workers of in mineralogy, and...

Celestial mechanics is the branch of mathematical astronomy devoted to studying the motions of celestial bodies subject to the Newtonian law of gravitation. This mathematical introductory textbook reveals that even the most basic question in celestial mechanics, the Kepler problem, leads to a cornucopia of geometric concepts: conformal and projective transformations, spherical and hyperbolic geometry, notions of curvature, and the topology of geodesic flows. For advanced undergraduate and ...

Chemists are used to the operational definition of symmetry, which crystallographers introduced long before the advent of quantum mechanics. The ball-and-stick models of molecules naturally exhibit the symmetrical properties of macroscopic objects. However, the practitioner of quantum chemistry and molecular modeling is not concerned with balls and sticks, but with subatomic particles: nuclei and electrons.This textbook introduces the subtle metaphors which relate our macroscopic u...

Since the year 2000, we have witnessed several outstanding results in geometry that have solved long-standing problems such as the Poincaré conjecture, the Yau–Tian–Donaldson conjecture, and the Willmore conjecture. There are still many important and challenging unsolved problems including, among others, the Strominger–Yau–Zaslow conjecture on mirror symmetry, the relative Yau–Tian–Donaldson conjecture in Kähler geometry, the Hopf conjecture, and the Yau conjecture on the first eigenvalue ...

In his foreword to Structural Mineralogy. An classification was taken into account. The first Introduction (Lima-de-Faria, 1994) P.B. Moore classification of this type, which takes into con emphasized that this book "is really not an end in sideration the distribution of bonds in a structure, itself. Rather it is a rallying call to urge further was that of silicates proposed by Machatschki clarification, representation and systematization (1928) and developed by Bragg (1930) and Naray of a...

Now in its second edition, this monograph explores the Monge-Ampère equation and the latest advances in its study and applications. It provides an essentially self-contained systematic exposition of the theory of weak solutions, including regularity results by L. A. Caffarelli. The geometric aspects of this theory are stressed using techniques from harmonic analysis, such as covering lemmas and set decompositions. An effort is made to present complete proofs of all theorems, and examples a...